To determine the width of the deck, we need to find the area of both the pool and the deck.
The area of the pool is given by length multiplied by width: 6m * 9m = 54m^2.
Since the area of the deck is the same as the area of the pool, the area of the deck is also 54m^2.
Let's assume the width of the deck is x.
The overall size of the pool and the deck together is increased by 2 times the width on each side.
So, the total dimensions of the pool and deck together would be (6 + 2x) by (9 + 2x).
The area of the pool and deck together would be (6 + 2x) * (9 + 2x).
Since the area of the pool and deck together is the same as the area of the pool, we can set up the following equation:
(6 + 2x) * (9 + 2x) = 54
Expanding the equation gives us:
54 + 12x + 18x + 4x^2 = 54
Combine like terms:
4x^2 + 30x + 54 = 54
Simplify:
4x^2 + 30x = 0
Factor out 2x:
2x(2x + 15) = 0
Set each factor equal to zero and solve for x:
2x = 0 or 2x + 15 = 0
If 2x = 0, then x = 0, but a deck with zero width is not possible.
So, if 2x + 15 = 0, then 2x = -15, and x = -7.5.
Since the width cannot be negative, we can discard the negative solution.
Therefore, the width of the deck is x = 0m.
Mr. Armstrong wishes to build a deck of uniform width around his pool. The pool is rectangular and has dimensions
6m by 9m. If the area of the deck is the same as the area of the pool, determine the width of the deck.
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